You could show that someone's abilities or values changed from one type to another over time (doesn't necessarily disprove socionics but the hypothesis that types remain the same)
You could show that someone has positive reactions to conflicting elements such as Te and Ti, Fe and Fi, etc. (This one seems pretty self-evident though since they are opposite priorities.)
In practice the model is still being refined and we deal with minor flaws (such as, misunderstandings of particular functions or dichotomies) by refining it. I haven't noticed any fatal contradictions as yet.